Question: The sum of two angles is $90^\circ$. Angle 2 is $51^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Answer: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 90}$ ${y = 2x-51}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-51}$ for $y$ in the first equation. ${x + }{(2x-51)}{= 90}$ Simplify and solve for $x$ $ x+2x - 51 = 90 $ $ 3x-51 = 90 $ $ 3x = 141 $ $ x = \dfrac{141}{3} $ ${x = 47}$ Now that you know ${x = 47}$ , plug it back into $ {y = 2x-51}$ to find $y$ ${y = 2}{(47)}{ - 51}$ $y = 94 - 51$ ${y = 43}$ You can also plug ${x = 47}$ into $ {x+y = 90}$ and get the same answer for $y$ ${(47)}{ + y = 90}$ ${y = 43}$ The measure of angle 1 is $47^\circ$ and the measure of angle 2 is $43^\circ$.